IDEAS home Printed from https://ideas.repec.org/a/spr/empeco/v54y2018i4d10.1007_s00181-017-1269-7.html
   My bibliography  Save this article

Loss modeling using Burr mixtures

Author

Listed:
  • S. A. Abu Bakar

    (University of Malaya)

  • Saralees Nadarajah

    (University of Manchester)

  • Z. A. Absl Kamarul Adzhar

    (University of Malaya)

Abstract

The first-ever real data application of a two-component Burr mixture distribution is provided. It is fitted to three loss data sets: fire loss claims in Denmark, fire loss claims for three building categories in Belgium and fire loss data in Norway. Each of these data sets exhibits significant bimodality. The fits of the two-component Burr mixture distribution are compared to those of five other two-component mixture distributions: the two-component Weibull mixture, two-component gamma mixture, two-component Pareto mixture, two-component lognormal mixture and the two-component exponential mixture distributions. The Burr mixture distribution is shown to give the best fit for each data set. The relative performances of the fitted distributions were assessed in terms of Akaike information criterion values, Bayesian information criterion values, consistent Akaike information criterion values, corrected Akaike information criterion values, Hannan–Quinn criterion values, density plots and probability–probability plots.

Suggested Citation

  • S. A. Abu Bakar & Saralees Nadarajah & Z. A. Absl Kamarul Adzhar, 2018. "Loss modeling using Burr mixtures," Empirical Economics, Springer, vol. 54(4), pages 1503-1516, June.
    • Handle: RePEc:spr:empeco:v:54:y:2018:i:4:d:10.1007_s00181-017-1269-7
    DOI: 10.1007/s00181-017-1269-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00181-017-1269-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00181-017-1269-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Resnick, Sidney I., 1997. "Discussion of the Danish Data on Large Fire Insurance Losses," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 139-151, May.
    2. Simon Lee & X. Lin, 2010. "Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 107-130.
    3. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    4. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    5. Jaeil Ahn & Bhramar Mukherjee & Stephen B. Gruber & Samiran Sinha, 2011. "Missing Exposure Data in Stereotype Regression Model: Application to Matched Case–Control Study with Disease Subclassification," Biometrics, The International Biometric Society, vol. 67(2), pages 546-558, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sarra Ghaddab & Manel Kacem & Christian Peretti & Lotfi Belkacem, 2023. "Extreme severity modeling using a GLM-GPD combination: application to an excess of loss reinsurance treaty," Empirical Economics, Springer, vol. 65(3), pages 1105-1127, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Semhar Michael & Tatjana Miljkovic & Volodymyr Melnykov, 2020. "Mixture modeling of data with multiple partial right-censoring levels," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 355-378, June.
    2. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    3. Bhati, Deepesh & Ravi, Sreenivasan, 2018. "On generalized log-Moyal distribution: A new heavy tailed size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 247-259.
    4. Reynkens, Tom & Verbelen, Roel & Beirlant, Jan & Antonio, Katrien, 2017. "Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 65-77.
    5. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
    6. N. V. Gribkova & J. Su & R. Zitikis, 2024. "Assessing the coverage probabilities of fixed-margin confidence intervals for the tail conditional allocation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 821-850, October.
    7. Rocco Roberto Cerchiara & Francesco Acri, 2020. "Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data," Risks, MDPI, vol. 8(3), pages 1-19, July.
    8. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    9. Arthur Charpentier & Emmanuel Flachaire, 2021. "Pareto Models for Risk Management," Dynamic Modeling and Econometrics in Economics and Finance, in: Gilles Dufrénot & Takashi Matsuki (ed.), Recent Econometric Techniques for Macroeconomic and Financial Data, pages 355-387, Springer.
    10. Farias, Rafael B.A. & Montoril, Michel H. & Andrade, José A.A., 2016. "Bayesian inference for extreme quantiles of heavy tailed distributions," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 103-107.
    11. Johan René van Dorp & Ekundayo Shittu, 2024. "Two-sided distributions with applications in insurance loss modeling," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 827-861, July.
    12. Bernard, Carole & Kazzi, Rodrigue & Vanduffel, Steven, 2020. "Range Value-at-Risk bounds for unimodal distributions under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 9-24.
    13. Laudagé, Christian & Desmettre, Sascha & Wenzel, Jörg, 2019. "Severity modeling of extreme insurance claims for tariffication," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 77-92.
    14. Sidney Resnick & Gennady Samorodnitsky, 2000. "A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements," Management Science, INFORMS, vol. 46(9), pages 1236-1248, September.
    15. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2021. "On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    16. Ahn, Soohan & Kim, Joseph H.T. & Ramaswami, Vaidyanathan, 2012. "A new class of models for heavy tailed distributions in finance and insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 43-52.
    17. Lee, David & Li, Wai Keung & Wong, Tony Siu Tung, 2012. "Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 538-550.
    18. John Sang Jin Kang & Serge B. Provost & Jiandong Ren, 2019. "Moment-Based Density Approximation Techniques as Applied to Heavy-tailed Distributions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(3), pages 1-1, November.
    19. Ioana Gutu & Daniela Tatiana Agheorghiesei & Alexandru Tugui, 2023. "Assessment of a Workforce Sustainability Tool through Leadership and Digitalization," IJERPH, MDPI, vol. 20(2), pages 1-30, January.
    20. Marianna Virtanen & Jussi Vahtera & Jenny Head & Rosemary Dray-Spira & Annaleena Okuloff & Adam G Tabak & Marcel Goldberg & Jenni Ervasti & Markus Jokela & Archana Singh-Manoux & Jaana Pentti & Marie , 2015. "Work Disability among Employees with Diabetes: Latent Class Analysis of Risk Factors in Three Prospective Cohort Studies," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-14, November.

    More about this item

    Keywords

    Loss; Maximum likelihood; Mixture distributions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:empeco:v:54:y:2018:i:4:d:10.1007_s00181-017-1269-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.